Need help with gaming on the Note 4

Just picked up a note 4 and seems like a huge upgrade from the Note 3 I had.
Gaming is a big factor on my phone, and wanted to get peoples input.
So far only game I've had problems with is DH5 with insane lagging even in situations where there are not many models on screen (monsters).

Some games lag and stutter on my Note 4. I believe it's the QHD screen. In clash of clans I lag sometimes whenever I'm raiding hard with tons of troops. Another game is Madden, but it has gotten better from updates. My Brother's note 3 doesn't lag at all in these games.

Things you wouldn't think of take TONS of computer resources - like the twinkling of a jewel or light reflecting off a shiny piece of metal that keeps moving, or the flickering of a fire. 500 moving people dressed in dark clothing on a dark night take less power to display than 1 twinkling jewel. Have a battle with weapons flaring and sunlight glancing off shiny objects and all but the most powerful graphics cards can lag. Some games don't push the envelope, they push through it.

Alright so far not too good in gaming for a premium smartphone. It seems to me that the hardware isn't capable of pushing the QHD screen with some of the more intensive games.
I've gotten lag on:
1. Dead Trigger 2. The game is set to medium quality as default... I had to manually set it to high, and got lag. (note 3 works fine on high while my nexus 9 can do ultra high.
2. Contest of Champions after 15 minutes, but went away quickly. Never lagged on nexus 9 or note 3.
3. DH 5 is the worst so far. Lags everywhere. Nexus 9 and Note 3 do not have this problem and are fine.

Just picked up a note 4 and seems like a huge upgrade from the Note 3 I had.
Gaming is a big factor on my phone, and wanted to get peoples input.
So far only game I've had problems with is DH5 with insane lagging even in situations where there are not many models on screen (monsters).

I get lag issues in the Simpsons Tapped Out when there are a bunch of the characters moving around on the screen (or maybe it's one part of the map, I haven't quite figured that out yet). This issue showed up immediately after upgrading to Lollipop, before that I never experienced the slowness / lagging issues (One exception - there was a known issue about frame rates and lag that they pushed an update out to fix, but it was before the Note 4 was released).